Closing the Gap: A Longitudinal, Covariate-Adjusted Analysis of NHL Goalie Pull Timing

Abstract

Down a goal in the closing minutes, an NHL coach can swap his goaltender for a sixth attacker - six skaters, no net, against the opponent's regular five. Eight regular seasons of play-by-play between 2015-16 and 2024-25 give us 7,047 such decisions. We pose four questions. Does pulling earlier actually produce more goals once we adjust for opponent, home ice, rest, and the rest of the obvious covariates? Have coaches as a group drifted earlier? Has the textbook one-goal optimum - the 2.75 min from Beaudoin and Swartz - itself moved under modern scoring rates? And if some franchises have closed the theory-practice gap, is the closure a league-wide phenomenon or the work of a small vanguard? Four causal estimators (covariate-adjusted regression, IPW, AIPW, fixed-effects Poisson) agree that earlier one-goal pulls raise post-pull scoring substantially; the E-value sits at 6.12. A simplified continuous-time Markov chain re-solved at 2024-era scoring rates places the one-goal optimum about a minute earlier than the original 2005 calibration - the target itself has drifted. League mean pull timing has crept earlier at six seconds per season and the pooled distribution stays unimodal, but team-level early-pull shares span 26-40 percentage points, worth between 0.5 and 3.2 standings points per team per season at the extremes. The vanguard has closed the gap; the median NHL franchise has not.